Question

Supervillain Prof. Marcia Grail is experimenting with energy and electric charge to better create a new doomsday weapon (and take over the world). She gathers a charge of 1.11 x 10^-10 C and places it in the center of a large empty spherical vacuum chamber of radius 250m (the place she fixes this immovable charge can be thought of as the origin of coordinates). The potential at a point 1m away in the positive y-direction is 1 V. What is the electric potential 1m away in the positive x-direction? What is the direction of the electric field at 1m away in the negative y-direction? What is the direction of the electric field at 1m away in the positive x-direction?

Answer 1

Ans

a) The charge is at the center of a larger spherical vacuum chamber, so the spherical surfaces with the charge at the center will be the equipotential surfaces. The points 1 m away in the positive y-direction and 1 m away in the positive x-direction are on the sphere of radius 1 m. So the electric potential at 1 m away in the positive x-direction is also equal to 1 V.

b) The electric field at 1 m away in the negative y-direction is in the negative y-direction. The electric field lines are normal to the equipotential surfaces and points in the direction of the decreasing potential.

c)The electric field at 1 m away in the positive-direction is in the positive x- direction. The electric field lines are normal to the equipotential surfaces and points in the direction of the decreasing potential.